If A is an empty set, how many elements are in P(P(A))?
Answer and explanation
Correct answer: 2
For an empty set A = ∅, its power set contains exactly one subset: P(A) = {∅}. This new set has one element, namely ∅. The power set of a one-element set has 2¹ = 2 elements: the empty subset and the set containing that one element. Thus P(P(A)) = {∅, {∅}}, so it contains two elements. The answer is not 1 because the second power-set operation is also required.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
For an empty set A = ∅, its power set contains exactly one subset: P(A) = {∅}. This new set has one element, namely ∅. The power set of a one-element set has 2¹ = 2 elements: the empty subset and the set containing that one element. Thus P(P(A)) = {∅, {∅}}, so it contains two elements. The answer is not 1 because the second power-set operation is also required.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
